The CFS explanation is certainly flawed in that it ignores the effect of downwash over the tailplane and the fact that zero lift angle of attack is rarely zero degrees. Like all classroom explanations it is a simplifcation that is used to make the subject more digestible, by limiting the number of variables being considered. But I believe that this makes the explanation incomplete rather than totally invalid.
The main function of the taiplane is to provide longitudinal stability. To do this its angle of attack must change as the aircraft pitches away from its trimmed condition.
As pointed out by MFS in his initial post, the downwash from the wing reduces the amount by which the talplane angle of attack changes as the aircraft pitches up or down. This reduces the stabilising effects of the tailplane.
This problem could be reduced by moving the tailplane to a different position such as on the top of the fin, where it will be less affected by the downwash from the wings. But longitudinal dihedral might provide an alternative solution to this problem.
To see how this might work we need to start by looking at a single aerofoil and simplify the matter by ignoring upwash and downwash. If we assume that the CL/Alpha graph is a straight line then each degree change in angle of attack will produce the same numerical change CL.
Let's suppose that this is plus 0.1 for each degree increase in alpha. If the aerofoil is initially at 4 dgrees above its zero lift angle, then its CL will be 4 x 0.1 = 0.4. If we increase the alpha by one degree we get a CL of 0.4 + (1 x 0.1) = 0.5. This represents a 25% increase in CL. If the aerofoil is being used as a tailplane (and we ignore changes in it C of P position) this will produce a 25% change in its contribution to the aircraft pitching moment.
Now imagine that the aerofoil is initially 2 degrees above its zero lift alpha. Its initial CL will be 0.2 and increasing alpha by 1 degree will produce a CL of 0.3. This is a 50% increase.
This means that the percentage by which CL changes for each degree change in angle of attack is greatest when the aerofoil is close to its zero lift angle.
It is possible that Longitudinal dihedral takes advantage of this effect by ensuring that the tailplane is closer than the wing, to its zero lift angle. I believe that this is the basis of the CFS explanation.
We can see the overall result if we now bring together the effects of downwash and longitudinal dihedral. The downwash from the wing reduces the amount by which the angle of attack of the tailplane varies as the aircraft pitches in flight. This reduces the stablising effect of the tailplane. Longitudinal dihedral increases the percentage by which tailplane lift changes for each degree change in its angle of attack. This compensates for the destabilising effects of the downwash from the wings.
It should be possible to vary the relative magnitudes of these two competing effects by adjusting the amount of longitudinal dihedral. For a logitudinally stable aircraft the stablising effect of the tailplane should increases as the deviation from the trimmed condition increases.
The use of trimmable tailplanes or stabilators, does not render the above argument invalid. As airspeed increases the downwash from the wings decreases. This reduces the amount of longitudinal dihedral that is required. This also enables us to minimise tailplane drag in cruise flight.